PLATCOV Statistical Analysis Plan
James Watson
18 February, 2022
TODO list:
- Add QC analysis (comparison of standard curves)
- Up and down model to account for the fact that subjects are in an increasing phase
- Data need to be also on the log viral copies per ml
- How much variance explained by the RNaseP
- Check missing data (vaccine/serology/age)
- Subgroup analysis model for temporal shift
- Define Epochs for the trial to get drift effects
- Model comparison using loo package
Preambule
This Statistical Analysis Plan (SAP) is written for the PLATCOV trial (registered at ClinicalTrials.gov: https://clinicaltrials.gov/ct2/show/NCT05041907).
Data preparation is done in a different R script called data_prep.R. This Markdown script assumes that the data are saved in two .csv file in long format.
The first file interim_control_dat.csv contains the PCR quality control data: CT values from the control samples from each plate (duplicate control samples of known viral densities over the range 100 to 10^7/mL viral copies per mL). This has the following headers:
- ID: unique control ID
- Plate: unique Plate ID for the PCR assay
- CT_NS: observed Ct value for the N/S gene
- log10_true_density: number of viral copies in control sample (log10 scale)
The second file interim_dat.csv contains the patient viral load data with the following column headers:
- ID: anonymised patient id code
- BARCODE: unique sample id code (in the following format: PLT-site-number-swab type-timepoint)
- Swab_ID: RTS or TSL (right versus left tonsil)
- Plate: unique Plate ID for the PCR assay (matching with plate identifiers in interim_control_dat.csv)
- Site: site at enrollment
- Trt: treatment allocation as written in CRF
- Time: time from randomisation
- Variant: variant of concern (using standard WHO terminology for the main lineages, reference will be the predominant variant in the dataset at the start of the study)
- Vaccinated: 0/1 (1: any number of doses and any manufacturer)
- Vaccine_type: manufacturer of vaccine dose 1 (AZ: astra zeneca; SPH: sinopharm; SV: sinovac; MD: moderna; PZ: pfizer)
- Antibody_test: 0/1 (positive/negative for SARS-CoV-2 antibody rapid test)
- Age: (years - has to be between 18-50)
- Sex: 0/1 (male: 1; female/other: 0)
- Symptom_onset: time since onset of symptoms (days)
- CT_NS: observed Ct value for the N/S gene
- CT_RNaseP: observed Ct value for the human RNase P gene
- log10_viral_load: log10 number of viral copies per mL (estimated from plat specific standard curve)
Setup
## _
## platform x86_64-apple-darwin17.0
## arch x86_64
## os darwin17.0
## system x86_64, darwin17.0
## status
## major 4
## minor 0.2
## year 2020
## month 06
## day 22
## svn rev 78730
## language R
## version.string R version 4.0.2 (2020-06-22)
## nickname Taking Off Again## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS 10.16
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] censReg_0.5-32 maxLik_1.5-2 miscTools_0.6-26
## [4] RColorBrewer_1.1-2 rstan_2.21.2 ggplot2_3.3.5
## [7] StanHeaders_2.21.0-7
##
## loaded via a namespace (and not attached):
## [1] bdsmatrix_1.3-4 Rcpp_1.0.7 lattice_0.20-44 prettyunits_1.1.1
## [5] ps_1.6.0 zoo_1.8-9 lmtest_0.9-38 assertthat_0.2.1
## [9] glmmML_1.1.1 digest_0.6.27 utf8_1.2.2 V8_3.4.2
## [13] R6_2.5.1 stats4_4.0.2 evaluate_0.14 pillar_1.6.2
## [17] Rdpack_2.1.3 rlang_0.4.11 curl_4.3.2 rstudioapi_0.13
## [21] callr_3.7.0 jquerylib_0.1.4 collapse_1.7.6 rmarkdown_2.11
## [25] stringr_1.4.0 loo_2.4.1 munsell_0.5.0 compiler_4.0.2
## [29] xfun_0.26 pkgconfig_2.0.3 pkgbuild_1.2.0 htmltools_0.5.2
## [33] tidyselect_1.1.1 tibble_3.1.4 gridExtra_2.3 codetools_0.2-18
## [37] matrixStats_0.61.0 fansi_0.5.0 crayon_1.4.1 dplyr_1.0.7
## [41] withr_2.4.2 rbibutils_2.2.7 MASS_7.3-54 grid_4.0.2
## [45] nlme_3.1-153 jsonlite_1.7.2 gtable_0.3.0 lifecycle_1.0.0
## [49] DBI_1.1.1 magrittr_2.0.1 scales_1.1.1 RcppParallel_5.1.4
## [53] cli_3.0.1 stringi_1.7.4 plm_2.6-0 bslib_0.3.0
## [57] ellipsis_0.3.2 generics_0.1.0 vctrs_0.3.8 sandwich_3.0-1
## [61] Formula_1.2-4 tools_4.0.2 glue_1.4.2 purrr_0.3.4
## [65] processx_3.5.2 parallel_4.0.2 fastmap_1.1.0 yaml_2.2.1
## [69] inline_0.3.19 colorspace_2.0-2 knitr_1.34 sass_0.4.0Load data and provide data summaries
## We have 720 PCR datapoints on 36 patients from 1 sites## Site
## Arm th001
## Favipiravir 8
## Ivermectin 7
## No study drug 7
## Regeneron 8
## Remdesivir 6## Age distribution of patients:## Site Age.mean Age.min Age.max
## 1 th001 30 21 49## Proportion male (%):## Site Sex
## 1 th001 100## [1] "!! WARNING - sex data made up as not in current clinical database that was sent !!"## Proportion vaccinated (%):## Site Vaccinated
## 1 th001 81## Vaccine type by site:##
## Site AZ None SPH SV
## th001 14 7 9 6## Number of days since symptom onset by site:## Sympom_Onset_days
## Site 1 2 3 4
## th001 14 11 10 1## Number of baseline viral load samples:##
## PLT-TH1-001 PLT-TH1-002 PLT-TH1-003 PLT-TH1-004 PLT-TH1-005 PLT-TH1-006
## 4 4 4 4 4 4
## PLT-TH1-007 PLT-TH1-008 PLT-TH1-009 PLT-TH1-010 PLT-TH1-011 PLT-TH1-012
## 4 4 4 4 4 4
## PLT-TH1-013 PLT-TH1-014 PLT-TH1-015 PLT-TH1-016 PLT-TH1-017 PLT-TH1-018
## 4 4 4 4 4 4
## PLT-TH1-019 PLT-TH1-020 PLT-TH1-021 PLT-TH1-022 PLT-TH1-023 PLT-TH1-024
## 4 4 4 4 4 4
## PLT-TH1-025 PLT-TH1-026 PLT-TH1-027 PLT-TH1-028 PLT-TH1-029 PLT-TH1-030
## 4 4 4 4 4 4
## PLT-TH1-031 PLT-TH1-032 PLT-TH1-033 PLT-TH1-034 PLT-TH1-042 PLT-TH1-045
## 4 4 4 4 4 4## [1] TRUE## In the 36 patients, the geometric mean baseline (defined as samples taken within 6 hours of randomisation) viral load was 291643 copies per mL (95 percentile interval from 1300 to 65433435; range from 370 to 76230035)
Data visualisation
Quality Control for PCR
## SD of the intercept is 0.52## Maximum difference in CT values for a tenfold change in viral load is 0.2
Overall data
RNaseP
## the standard deviation of the RNaseP CT distribution is 1.26.## 95% of the distribution is within 4.92 CT values differenceModel fitting
Main models: Bayesian hierarchical models with and without covariate adjustment. All models adjust for human RNaseP quantification (scaled to have mean 0).
Covariates that we use in model 2:
- Vaccination (yes/no)
- Time since symptom onset (days)
- Variant (made up data)
- Serology rapid test (+/-)
Specify priors
## $A0_prior_mean
## [1] 18
##
## $A0_prior_sd
## [1] 5
##
## $alpha_prior_mean
## [1] -2
##
## $alpha_prior_sd
## [1] 2
##
## $sigma_trt_effect
## [1] 0.5Prepare model
compile model in stan
make stan data set
## Total number of datapoints up until day 8 is 648Run models
run models
## Warning: There were 2 divergent transitions after warmup. Increasing adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup## Warning: Examine the pairs() plot to diagnose sampling problems## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#tail-essModel fits: summaries
## mean se_mean sd
## A0 15.59702468 0.022097510 0.60486781
## alpha -1.55513326 0.008534694 0.23770647
## trt_effect[1] -0.12349436 0.008216898 0.21680978
## trt_effect[2] -0.18421896 0.008128133 0.23116343
## trt_effect[3] 0.03530532 0.008262219 0.22618872
## trt_effect[4] -0.28992107 0.008306994 0.22280697
## sigmaCT 2.76514261 0.005257483 0.15625396
## t_dof 4.24553065 0.030799762 0.88629362
## gamma_rnasep 0.61207607 0.005090706 0.14137562
## sigma_plate 0.46948595 0.004398391 0.12834999
## sigmasq_u[1] 3.10789550 0.014524483 0.41953654
## sigmasq_u[2] 0.46798625 0.002985289 0.08366125## mean se_mean sd
## A0 15.48982757 0.020192251 0.55578496
## alpha -1.48491231 0.008606630 0.24665477
## trt_effect[1] -0.08891000 0.008974062 0.23486123
## trt_effect[2] -0.27911215 0.008524743 0.24769692
## trt_effect[3] 0.02702020 0.008458358 0.24551768
## trt_effect[4] -0.30815815 0.008808810 0.23819128
## sigmaCT 2.82548131 0.005607236 0.15244860
## t_dof 4.31963425 0.032490185 0.89971666
## gamma_rnasep 0.06180949 0.033906488 0.95703557
## sigma_plate 0.47180664 0.004422641 0.13216581
## sigmasq_u[1] 3.02138770 0.014120854 0.40460707
## sigmasq_u[2] 0.51894263 0.003717863 0.09512628## mean se_mean sd
## A0 18.31985034 0.047624662 1.18095757
## alpha -1.50830118 0.024970259 0.52053121
## trt_effect[1] -0.10875017 0.009377879 0.21786808
## trt_effect[2] -0.16257121 0.009581008 0.23245511
## trt_effect[3] 0.09959289 0.015913977 0.25984214
## trt_effect[4] -0.25535884 0.015090239 0.23688704
## sigmaCT 2.77592102 0.005680938 0.15580236
## t_dof 4.25974008 0.031165005 0.87990725
## gamma_rnasep 0.61795092 0.006084076 0.15011465
## sigma_plate 0.46113897 0.004355924 0.13052445
## sigmasq_u[1] 2.78633554 0.013974384 0.37964871
## sigmasq_u[2] 0.49012577 0.003639807 0.09168617
Results
Estimated treatment effects: no covariate adjustment
Posterior distributions over the treatment effects for the interventions. Red: no effect; blue: median inferred effect.
## Regeneron Ivermectin Remdesivir Favipiravir
## 0.8838266 0.8317537 1.0359359 0.7483226## Probability that Regeneron increases the viral clearance slope by more than 5%: 0.21## Probability that Ivermectin increases the viral clearance slope by more than 5%: 0.15## Probability that Remdesivir increases the viral clearance slope by more than 5%: 0.48## Probability that Favipiravir increases the viral clearance slope by more than 5%: 0.06
Estimated treatment effects: with covariate adjustment
Posterior distributions over the treatment effects for the interventions, after adjustment for the key covariates (. Red: no effect; blue: median inferred effect.
## Regeneron Ivermectin Remdesivir Favipiravir
## 0.8969545 0.8499556 1.1047211 0.7746385## Probability that Regeneron increases the viral clearance slope by more than 5%: 0.26## Probability that Ivermectin increases the viral clearance slope by more than 5%: 0.18## Probability that Remdesivir increases the viral clearance slope by more than 5%: 0.58## Probability that Favipiravir increases the viral clearance slope by more than 5%: 0.1
Estimated covariate effects
RNaseP
Gamma is the parameter
Other covariates
Individual fits
Individual plots. Thick line no covariate adjustment; dashed line covariate adjustment.
Sensitivity analysis
Left vs right tonsil
Basic slope - individually fit
Use left censored linear regression
